552 citations · 2k across the 45 of their papers we have counts for
18 papers · 1 filter
On the notion of Laplacian bounds on spaces and applications
Nicola Gigli, Andrea Mondino, Daniele Semola
We show that several different interpretations of the inequality are equivalent in the setting of spaces. With respect to previously available results…
Weakly non-collapsed RCD spaces are strongly non-collapsed
Camillo Brena, Nicola Gigli, Shouhei Honda +1
We prove that any weakly non-collapsed RCD space is actually non-collapsed, up to a renormalization of the measure. This confirms a conjecture raised by De Philippis and the second…
Parallel transport on non-collapsed spaces
Emanuele Caputo, Nicola Gigli, Enrico Pasqualetto
We provide a general theory for parallel transport on non-collapsed spaces obtaining both existence and uniqueness results. Our theory covers the case of geodesics and,…
Monotonicity formulas for harmonic functions in spaces
Nicola Gigli, Ivan Yuri Violo
We generalize to the setting a family of monotonicity formulas by Colding and Minicozzi for positive harmonic functions in Riemannian manifolds with non-negative R…
Global Lipschitz extension preserving local constants
Simone Di Marino, Nicola Gigli, Aldo Pratelli
The intent of this short note is to extend real valued Lipschitz functions on metric spaces, while locally preserving the asymptotic Lipschitz constant. We then apply this results…
Rigidity for the spectral gap on -spaces
Nicola Gigli, Christian Ketterer, Kazumasa Kuwada +1
We consider a rigidity problem for the spectral gap of the Laplacian on an -space (a metric measure space satisfying the Riemannian curvature-dimension condition) fo…